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Explaining International Business Cycle Synchronization: Recursive Preferences and the Terms of Trade Channel

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Abstract

The business cycles of advanced economies are synchronized. Standard macro models fail to explain that fact. This paper presents a simple model of a two-country, two-traded-good, complete-financial-markets world in which country-specific productivity shocks generate business cycles that are highly correlated internationally. The model assumes recursive intertemporal preferences (Epstein-Zin-Weil), and a muted response of labor hours to household wealth changes (due to Greenwood-Hercowitz-Huffman period utility and demand-determined employment under rigid wages). Recursive intertemporal preferences magnify the terms of trade response to country-specific shocks. Hence, a productivity (and GDP) increase in a given country triggers a strong improvement of the foreign country’s terms of trade, which raises foreign labor demand. With a muted labor wealth effect, foreign labor and GDP rise, i.e. domestic and foreign real activity comove positively.

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Notes

  1. Other related International RBC models include Dellas (1986), Cantor and Mark (1988), Crucini (1989), Devereux et al. (1992), Kollmann (1991, 1996), Schmitt-Grohé (1998) and Heathcote and Perri (2002).

  2. CRA > 1/IES implies a preference for the early resolution of uncertainty over future consumption (Weil 1990).

  3. In response to the Home productivity increase, Foreign life-time utility rises too, but less than Home life-time utility (due i.a. to the local spending bias); thus, the relative Home/Foreign IMRS falls.

  4. Benigno et al. (2012), Mumtaz and Theodoridis (2015) and Backus et al. (2016) study the effect of volatility shocks. Kollmann (2010) and Tretvoll (2016) analyze determinants of real exchange rate variability, while Colacito et al. (2014) explore differential effects of permanent and transitory productivity shocks on international capital flows. Only the latter three papers report model-predicted international correlations – those papers fail to capture the simultaneous high empirical cross-country correlations of output, labor and investment.

  5. In the numerical simulations, b is set at a very small value, which implies that the term βi,tΨi,t + 1/Ψi,t in (4) makes a negligible contribution to high-frequency fluctuations of ρi,t + 1.

  6. Concavity of the KPR period utility function requires ζ´´ < (2 − 1/σ)(ζ´)2/ζ.

  7. Under GHH utility, the disutility of labor is scaled by Xi,t to permit balanced growth, and to ensure that equilibrium hours worked are stationary; the Xi,t term can be rationalized by assuming that there is household home production (e.g., Rudebusch and Swanson (2012)). KPR period utility is consistent with balanced growth and stationary hours when the disutility of work is not scaled by productivity.

  8. Holding consumption constant, a rise in the wage rate w induces an increase in desired labor supply, as -ζ’/ ζ is increasing in hours worked; for a given wage rate w, a rise in consumption lowers desired hours worked (negative wealth effect), under KPR period utility.

  9. Rigid-wage models usually assume that hours are demand-determined (e.g., Blanchard and Gali 2007; Kollmann et al. 2016).

  10. The small value of b implies that short term model dynamics are similar to those generated by a (non-stationary) model variant with a constant subjective discount factor (b = 0).

  11. Under KPR period utility, the Frisch labor supply elasticity (LSE), evaluated at the steady state, is LSE=1/(1/η+ω/sC), where η is the curvature of labor disutility (see (7)) and sC is the steady state consumption/GDP ratio. sC depends solely on ω,δ and \( \overline{\beta} \). Under GHH utility, LSE = η.

  12. The 13 ROW countries are: Australia, Austria, Canada, Finland, France, Germany, Ireland, Italy, Japan, Korea, Norway, Sweden, UK. The Ohanian-Raffo quarterly labor hours data (available until 2013) are estimated from time series on employment and hours worked per employee (ILO, OECD).

  13. In the model, the share of GDP going to labor equals ω; the sample average of the labor share (compensation of employees/(GDP net of indirect taxes)) is 0.64 (0.66) in the US (ROW).

  14. I construct empirical log productivity (labor augmenting) for country i as ln(θi, t) = ( ln(GDPi, t) − ωi ln(Li, t) − (1 − ωi) ln(Ki, t))/ωi, where ωi is the sample average of i’s labor share. The labor input measure is total hours worked; quarterly capital series are cubic spline interpolates of annual capital stocks from the Penn World Table. A Törnqvist index is used to construct aggregate ROW productivity, θROW,t: \( \varDelta \kern0em \ln \kern0em {\theta}_{ROW,t}={\sum}_{j=1}^{13}{s}_{j,t}\varDelta \kern0em \ln {\theta}_{j,t} \) where sj,t is the weight of country j at date t, with ∑j sj,t = 1. The weights are countries’ smoothed nominal GDP shares in aggregate ROW nominal US$ GDP, at current exchange rates (to reduce the effect of nominal exchange rate volatility, exponential time trends are fitted to raw GDP shares, and fitted trend shares are used as weights).

  15. ROW aggregates for GDP, C, I and L (hours worked) are Törnqvist indices (GDP-weighted) of individual countries’ series. The ROW NX/GDP series is a GDP-weighted average of individual countries’ NX/GDP.

  16. Based on returns data from Ken French’s data base. The Sharpe ratio of an asset is the ratio of the mean of its excess return (relative to a risk-free asset) divided by its standard deviation.

  17. Consumption is countercyclical in model variants with KPR period utility and recursive intertemporal preferences (see discussion below).

  18. With recursive preferences and KPR period utility, Home consumption actually falls on impact. This explains why consumption is countercyclical, in that model configuration, as mentioned above.

  19. The stronger initial rise in Home GDP, under a predetermined consumption wage rate, explains why the predicted standard deviation of output (about 1.4%) is higher than in a flex-wage structure. Also, the predicted relative standard deviation of hours worked is now larger than the empirical relative standard deviation. By contrast, the flex-wage model variants yield a relative volatility of hours worked that is below empirical relative hours volatility.

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Acknowledgements

I thank Giancarlo Corsetti, Nelson Mark, Kemal Özhan, Vincenzo Quadrini, Werner Roeger, Gauthier Vermandel, Roland Winkler and workshop participants at Fed Board of Governors, Dallas Fed, IMAC3, Korea University, MACFINROBODS, SED, Swiss National Bank and Bank or England for useful comments and discussions. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7) under grant agreement no. 612796, Project MACFINROBODS (‘Integrated Macro-Financial Modelling for Robust Policy Design’).

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Authors and Affiliations

  1. European Centre for Advanced Research in Economics and Statistics (ECARES), Université Libre de Bruxelles, 50 Avenue Roosevelt, 1050, Brussels, Belgium

    Robert Kollmann

  2. Centre for Economic Policy Research (CEPR), 33 Great Sutton Street, London, EC1V 0DX, UK

    Robert Kollmann

  3. Université-Paris Est Créteil, 61 Avenue du Général de Gaulle, 94010, Créteil, France

    Robert Kollmann

  4. Globalization and Monetary Policy Institute (Federal Reserve Bank of Dallas), 2200 N Pearl Street, Dallas, TX, 75201, USA

    Robert Kollmann

  5. Centre for Applied Macroeconomic Analysis (CAMA), Australian National University, Lennox Crossing, Canberra, ACT, 0200, Australia

    Robert Kollmann

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Kollmann, R. Explaining International Business Cycle Synchronization: Recursive Preferences and the Terms of Trade Channel. Open Econ Rev 30, 65–85 (2019). https://doi.org/10.1007/s11079-018-9515-y

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